Donald Trump still doesn’t have a single governor or member of Congress endorsing his bid for the White House — a stunning shutout for the Republican Party’s national front-runner that underscores just how anathema he remains even for the most die-hard anti-Washington lawmakers.

Even lawmakers who have spoken well of Mr. Trump have either backed another candidate or say they will stay neutral. That leaves the billionaire businessman, along with retired neurosurgeon Ben Carson, as the only two major Republican candidates without top-level endorsements.

Former Florida Gov. Jeb Bush leads the pack with the most endorsements, but he hasn’t won any new ones in more than a month, according to the count maintained by FiveThirtyEight.com.

Instead, all the action appears to be with Sen. Marco Rubio, a Florida Republican who is racking up backing from both establishment and conservative Republicans, and Sen. Ted Cruz, a Texan who is steadily drawing support from conservative House lawmakers — including three more this week.

“If endorsements mattered, Jeb Bush would be in first place,” said Hope Hicks, his spokeswoman. “We have received many prominent endorsements from elected officials and public figures; however, the only endorsement we are seeking is that of the American people, and Mr. Trump is the definitive front-runner for the Republican nomination.”

Indeed, one reason for his shutout is that he doesn’t have the kinds of deep political relationships that the other Republicans have with fellow politicians in Washington.

Mr. Bush, for one, can tap into years of good will he has built up over years along with two former presidents — his father and his brother. But Mr. Trump says those kinds of deep political ties come with a price — the expectation that candidates will be beholden to their well-heeled backers.

Mr. Trump has proved a conundrum for Republicans since he announced his bid in June, confounding party leaders with his brash style and abrasive rhetoric but thrilling a large number of potential primary voters who like him precisely because he irks the party’s leadership.

That was on display Tuesday night when South Carolina Gov. Nikki Haley, who has not endorsed anyone in the presidential race, blasted Mr. Trump in the official Republican response to President Obama’s State of the Union address.

“During anxious times, it can be tempting to follow the siren call of the angriest voices. We must resist that temptation,” she said in her speech.

She acknowledged Wednesday that the reference was to Mr. Trump and to others.

Strategists said the antipathy goes both ways.

“He is too toxic for members to endorse, and I am pretty certain he hasn’t asked for any,” said John Feehery, a Republican Party strategist. “He is a complete outsider, and it seems to be working for him.”

Mr. Trump has consistently held a colossal lead over his competitors in polling in New Hampshire and appears to be surging again in Iowa, with surveys this week showing he has pulled even with Mr. Cruz.

Mr. Cruz this week announced that he has been endorsed by Phil Robertson, star of the “Duck Dynasty” program, who called the senator from Texas a “godly” person. Mr. Robertson also said Mr. Cruz “would kill a duck and put him in a pot and make him a good duck gumbo.”

Although individual endorsements may not swing a race, the numbers-crunchers at FiveThirtyEight.com, a statistics-heavy website that follows politics and sports, said the winner of the “endorsement primary” is often the winner of the nomination, but only if the lead over the competition is overwhelming.

This is not one of those years, according to the website’s calculations, which weigh governors’ endorsements at 10 points, senators’ endorsements at five points and House members’ backing at one point each. Mr. Bush has amassed 30 total endorsements, earning him 46 points. Mr. Rubio is second with 27 endorsements, totaling 43 points in the website’s “endorsement primary.”

By contrast, George W. Bush had amassed more than 500 endorsement points at the time of the Iowa caucuses in 2000. Former Secretary of State Hillary Clinton has more than 450 points now as she seeks the Democratic presidential nomination.

One striking difference between Mrs. Clinton’s primary and the Republican battle is how complimentary Democrats are to their entire field, including Mrs. Clinton and fellow candidates Sen. Bernard Sanders and former Maryland Gov. Martin O’Malley.

By contrast many Republican officeholders have little nice to say about Mr. Trump — and he returns the vitriol.

There have been exceptions.

Rep. Dave Brat, the Virginia Republican who unseated Majority Leader Eric Cantor in a 2014 primary, attended a rally Mr. Trump held in Virginia and received a special shoutout from the stage. But Mr. Brat has remained neutral in the Republican primary competition, saying he has a number of friends involved, including Mr. Carson, Mr. Cruz, Mr. Trump and Sen. Rand Paul, who campaigned for Mr. Brat in the 2014 race.

“I’m supportive of all of our candidates, and I’m not going to pick a single horse,” he told The Washington Times.

Rep. Louie Gohmert has said he is a fan of Mr. Trump’s but is backing his fellow Texan, Mr. Cruz.

“I have talked with Mr. Trump,” Mr. Gohmert said. “I am impressed with his business savvy and acumen, am thrilled he recognizes the biggest problems facing America, but I endorsed Ted many months ago because I agree with him on more issues than anyone and know he can stand up to the greatest pressure from both sides of the aisle when he knows something is critical for our nation.”

The closest Mr. Trump has to an endorsement is Sen. Jeff Sessions, an Alabama Republican who is particularly influential on immigration issues and who led opposition to the 2013 Senate bill championed by Mr. Rubio that would have granted citizenship rights to most illegal immigrants.

Mr. Sessions has endorsed Mr. Trump’s immigration plan, and they share a vehement opposition to the Trans-Pacific Partnership trade deal Mr. Obama negotiated last year. But an aide said Mr. Sessions has never endorsed anyone in a presidential primary during his two decades in Congress.

“However, he believes strongly that whoever is the GOP nominee must commit to defending working Americans from reckless trade and immigration policies that are sending their jobs and wages overseas,” the Sessions aide said. “This election will decide whether the forces who pushed amnesty in 2013 and Obamatrade in 2015 are running the White House in 2017.”